0=19x+0.10x^2

Solution for 0=19x+0.10x^2 equation:

0=19x+0.10x^2

We move all terms to the left:

0-(19x+0.10x^2)=0

We add all the numbers together, and all the variables

-(19x+0.10x^2)=0

We get rid of parentheses

-0.10x^2-19x=0

We add all the numbers together, and all the variables

-0.1x^2-19x=0

a = -0.1; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-0.1)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-0.1}=\frac{0}{-0.2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-0.1}=\frac{38}{-0.2}
=-190
$